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David DrasinDepartment of Mathematics, Purdue UniversityPekka PankkaDepartment of Mathematics and Statistics, P.O. Box 68, (Gustaf Hällströmin katu 2b), University of Helsinki, Finland
We show that given $${n \geqslant 3}$$ , $${q \geqslant 1}$$ , and a finite set $${\{y_1, \ldots, y_q \}}$$ in $${\mathbb{R}^n}$$ there exists a quasiregular mapping $${\mathbb{R}^n\to \mathbb{R}^n}$$ omitting exactly points $${y_1, \ldots, y_q}$$ .
Björn AndreasMathematisches Institut, Freie Universität BerlinDarío Sánchez GómezDepartamento de Matemáticas and Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de SalamancaFernando Sancho de SalasDepartamento de Matemáticas and Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca
We construct relative and global Euler sequences of a module. We apply it to prove some acyclicity results of the Koszul complex of a module and to compute the cohomology of the sheaves of (relative and absolute) differential $p$ -forms of a projective bundle. In particular we generalize Bott’s formula for the projective space to a projective bundle over a scheme of characteristic zero.